As is well known, there are several types of monochromators. The SEYA-NAMIOKA device is of particular interest beacuse the entrance and exit slits are fixed and the grating is also fixed with respect to the slits, the grating being subjected only to rotation in order to scan the spectral range of interest. However, this instrument suffers from a very severe constraint in that the angle 2.theta. between the axes of the two slits is fixed (approximately 70.degree.30') if the instrument is to have reasonable resolution.
In my copending application Serial No. 537,460, now U.S. Pat. No. 4,036,558 a continuation-in-part of Ser. No. 277,857, filed Aug. 4, 1972 and now abandoned, a technique is disclosed by which the angular constraint of the SEYA-NAMIOKA mounting is removed while at the same time improving the optical performance by achieving increased resolution and luminosity.
Basically, these improvements are achieved by a second order focusing condition in which aberration terms of higher order are compensated by the use of phase balancing and of image-evaluation criteria, involving shifts off of the Gaussian image plane as a function of aberrations of higher order.
In my copending application Ser. No. 497,940, now U.S. Pat. No. 3,973,850 filed Aug. 16, 1974 even further optical improvements are achieved. Specifically, a technique is disclosed which involves determining the physical parameters of the mounting using a classical grating (i.e. a spherically concave grating having parallel and equidistantly spaced grooves) based upon the aforesaid second order focusing condition. Then, using these same physical parameters the classical grating is replaced by a holographically formed grating in which the physical parameters employed in the holographic recording of the grating are used at least partially to correct for residual astigmatism.
Basically, the technique involves implementation of Fermat's principle: ##EQU1## where F.sub.1 and F.sub.2 respectively are the optical path contributions associated with the classical grating and with the holographic formation of the substituted grating, and where w and l respectively are the Cartesian coordinates with respect to the center of the grating perpendicular and parallel to the axis of grating rotation. The aforesaid second order focusing condition is equivalent to .differential.F.sub.1 /.differential.w=0. Therefore, the conditions .differential.F.sub.2 /.differential.w=0 and ##EQU2## are employed to determine physical positions of the laser point sources used holographically to form the substitute grating so that phase variation is generated over the holographic grating which at least partially balances the residual astigmatism associated with the classical grating. It being well known that astigmatic correction leads to increase in the principal coma terms, the aforesaid conditions may also be employed partially to correct these coma terms. Because there is improved optical performances with respect to astigmatism and coma, a further increase in resolution and luminosity is achieved with respect to the mounting disclosed in the first mentioned applications.
There are many instances where still further improvements are needed. For example, in vacuum ultraviolet (VUV) diagnostics of plasma, i.e., as generated by a Tokomak machine, Doppler and Stark broadening measurements of line widths as a function of time lead to ion temperature and ion number density determinations. Also, determination of electronic temperature and relative species number densities can be performed using line ratio techniques. In the former cases, high resolution is required and in all of the above cases disymmmetrical broadening of the image due to insufficient optical performance of the instrument must be avoided. In spectroscopic devices employing concave diffraction gratings, this latter objective can be attained only if coma as well as astigmatism is well corrected. Pieuchard et al [see French patent 6908883, U.S. Pat. No. 3,628,849, Jobin et Yvon's catalogue: Holographically Produced Diffraction Gratings- Technical Guide, Ordering Information, and Grating Lists (1972), G. Pieuchard and J. Flammand: Final Report of Jobin et Yvon to the Goddard Space Flight Center, NASA (1972), J. Cordelle, J. Flammand G. Pieuchard and A. Labeyrie: Optical Instruments and Techniques, Ed. J. Home Dickson, Oriel Press, Newcastle, (1970) p. 117] have employed holographically formed gratings using the stigmatic Weierstrass points of the sphere to obtain stigmatic correction at wavelengths proportional to the laser wavelength used holographically to form the grating. Because the lowest usable laser wavelength is about 4886A, it is impossible to use this type of solution in the spectral range of 200-2500A which is of paramount interest. Moreover, such solution is not adapted to construct a SEYA-NAMIOKA type instrument, i.e., one having fixing entrance and exit slits and a grating which is also fixed except for rotation to scan the spectral range of interest.
In the realm of grazing incidence instruments, monochromators have been constructed with classical gratings as well as toroidal gratings having parallel and equidistantly spaced grooves [R. J. Speer, D. Turner, R. J. Johnson, D. Rudolph and G. Schmahl, Appl. Opt. 13, 1259 (1974]. In such type of devices, either the exit slit or the grating must move on the Rowland circle, requiring very complex mechanical mounting and suffering from the severe disadvantage that the exit beam direction is not fixed. Greiner as well as Namioka [H. Greiner and E. Schaffer, Optik, 16, 288,350 (1959) and T. Namioka, J. Opt. Soc. Am., 50, 4(1960); 51, 13,(1961)] have investigated the SEYA-NAMIOKA mounting using a toroidal grating with parallel and equidistantly spaced grooves. However, such instruments do not allow investigation of wavelengths below about 200A because it is necessary to increase the angle 2.theta. with respect to the angle of 70.degree.30' characteristic of the SEYA-NAMIOKA mounting in order to increase the reflectivity of the instrument. By using a toroidal grating having a non-uniform groove distribution, Lepere [D. Lepere, Nouv. Rev. Opt., 6, 173 (1975)] has proposed a SEYA-type instrument having an angle of 142.degree. between the entrance and exit beams, allowing the possibility of investigating wavelengths down to about 150A. In my copending application Serial No. 497,940, filed Aug. 16, 1974 the possibility of designing grazing incidence monochromators involving a simple rotation of spherical or toroidal grating has been also pointed out but the solutions are not restricted to a specific .theta. value. In particular, more grazing incidence monochromators can be designed, which are very useful for laser plasma diagnostics.